Robust Superdirective Beamforming Under Uncertainty Set Constraint

Abstract

Based on gain optimization methods, superdirective beamformers can achieve high beam directivity with small aperture array. However, the extreme sensitivity to array uncertainty is a main obstacle to engineering application. In this work, a robust gain optimization algorithm under uncertainty set constraint is proposed. Considering steering vector mismatch is the result of combined effect of various array errors, and it is a measurable indicator especially in receiving system. We apply its uncertainty as a constraint on gain optimization method, which is more intuitive in physical sense. Different from existing solutions, it makes a better tradeoff among directive gain, robustness and radiation efficiency. Experimental analysis verifies its good performance in engineering.

A Set of Simple Numerical Pattern Synthesis Algorithms for Anti-Jamming With Superdirective Receiving Array

“…Still revolving around robustness problem, Ref. [10] proposes a uncertainty-constrained optimal directive gain (U-CODG) method. Considering steering vector mismatch always exists in real array system, we can only get its estimate.…”

“…As seen, the solution is very similar to S-CODG method. In Formula (10), matrix R can further be decomposed as R = UΛU H , in which U represents the eigenvector matrix, and Λ is a diagonal matrix composed by the eigenvalues of R. Make z = U H a(θ 0 , φ 0 ). Based on the analysis of [10], by choosing a proper mismatch value of μ/ z 2 , the same robustness and efficiency can be acquired as S-CODG method.…”

“…Zhang et al apply steering vector mismatch to model the uncertainty of a super-gain array. Most of these approaches can be classified as diagonalloading method [6][7][8][9][10]. Based on these theoretical contributions, superdirective arrays gradually enter engineering application stage.…”